I wish I could tell you all the grammar in this sentence, but it would take quite a while. I’m not sure if you want parts of speech, a diagram of the sentence, or what. So . . . since I’m in the dark, I’ll give you the Reader’s Digest Condensed Version. First, this sentence is correct. Second it is a tricky simple sentence with the primary clause being “Archaeologists plan to remove the mummy of Tutankhamen” and a subordinate clause “to solve the mystery of his death.” It contains five nouns, three verbs, several prepositions, one pronoun, and one punctuation mark. And it could be changed considerably with the addition of the word “and” after the word “Tutankham.” If this is not what you wanted, let me know.